Note 12/2012: This is the 2nd page from Jim with details regarding how to use his spreadsheet to save the details needed for the FMS 2 alpha 8 POLAR into the FMS .par file.

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From: John Cole
To: GaryG51384
Subject: Re: How to build a .par file
Date: Tue, Feb 9, 2010 6:42 am

Building a spreadsheet is quite straightforward for the main part of the polar data (that is, excluding the three flow-separation lines), and that's exactly how I produced my data. To generate the whole par file in one go would I think be complicated unless you simply put in all the non-polar data as constants. So here's my spreadsheet so you can put your own data in for any other aerofoil, once you've read this note.

I'm retired and when I bought my PC 8 years ago (on retirement) I did not feel like paying for Excel; my PC came with Works - so I've just used the very-basic Works spreadsheet. It may be that you can do more with Excel, but here's the spreadsheet I actually used. I've exported it in Excel format (and looked at it with an Excel viewer and it looks OK to me, but it doesn't show the formulae) so you should be able to open it OK. I've included both the xls and xlr versions, so if the xls version's wrong, try opening the xlr version (as Works Spreadsheet, I expect). All it does is collect the data for the lines (26 in my wing polar) of alpha, Cl, Cd and Cm.

Columns A,B, F and P are the 360-degree data from Sandia for alpha, Cl, Cd and Cm. You'll see I labelled these Symm for symmetric, and used the label Cdp for (parasitic) drag. If you look at their report you'll find you need to dig round to find the Cm graph as it's separate from the rest. You'll see I've put in some additional rows with no Sandia data shown - just the Alphas. That's because I e.g. put in column C the E374 data from the Simons book, and used extra values of alpha for that. Column D contains a formula: Use the column C data unless it's blank, in which case use the column B data: in Works the formula is =IF(C26="",B26,C26) So now column D contains the combined Cl data from Sandia (naca 15) and Simons (e374), for an infinite wing. Columns F, G and H do the same trick for Cdp.

Columns J K and L initially bring together these results so j5 = a5, k5 = d5 and l5 = h5. But if you look at rows 27 to 33 where e.g. A33 = 17 degrees you'll find they don't match: J33 = 20.8 degrees. That's because for those rows the formula is not j5=a5 but J33=(A33-A$26)*1.2+A$26 - that's how I flatten the Cl / alpha curve by 20% to reflect in-flow / out-flow. That's why the column is headed Alpha A(spect) R(atio) modified. I only did it for that narrow range; I could have done it for a wider range. But I didn't!

Column M calculates the vortex-induced drag (Cdi), and N adds the 2 drag components together. The formula for Cdi is Cl * Cl /( pi * AR) or =K5*K5/(PI()*6) for AR = 6.

FMS will (I think) calculate data values for points between the values of alpha in the polar assuming straight lines. For the normal range that's mainly OK as until you get to the stall, Cl varies linearly with alpha, Cd is constant and Cm is either constant or varies linearly. These relations break down at the stall which is why I put some extra points in around the positive and negative stall. But Cdi varies with Cl squared and is not linear. That's why I put an extra row in (uncorrected alpha of 6 degrees) to let that non-linearity appear in the polar.

So now we have all the data to write the polars (except the three "separation" lines). I've explained about the wing polar, but for the stab / fin polars (I used the same data for the two polars, called here Tail) I've just used the Sandia data (I did not bother calculating Cdi or correcting alpha for AR). Columns W X Y and Z bring them together.

There's only one further complication: that not all the rows are complete - and you can only enter complete rows in the polar. That's because I only put in Cm values where I thought it mattered! So we're not going to put in data for rows alpha = -130 to -100 degrees. FMS can interpolate for this unimportant region. So now in columns R to U for the wing (and AB to AE for the tail) I get rid of the "partial" lines. If you look in R1 you'll see the "hidden" formula =IF($O1="","",J1) What this means is that if there's no Cm value, leave Alpha blank, and as there's no data in row 1 the result is "" or blank: it's not DELIBERATELY hidden.

There are similar formulae in S T1 and U1, and AB1 to AE1 for the tail. These are "spare" copies of the formula, which you now copy and paste into J5 to U49. You now have (complete) rows of data only where there's a Cm value. Then highlight R5 to U49 and copy / paste special so you paste the VALUES back into these cells. Then Sort this block (on column R, alpha). Now you can see why there's a spare copy of the formulae in row 1, as there are no formulae in the sorted block, only numbers.

I'm not sure if in Excel the blank lines will sort above or below the numeric cells. If above, cut the numeric block and paste it back starting in R5 (or initially do a reverse-order sort, then select just the (top) numeric rows and normal-sort them). Now R5 to U30 will contain the data for the wing polar except R4 needs to contain the number of rows: this is (R)30-(R)5 +1, = 26 in this case. You do the same for the Tail data, but note that the blank-line-omitter formula is =IF(OR($Z1="",$X1=""),"",W1)

To get just this block of wing data into the par file I first saved the spreadsheet, then created another one and copied the block R4 to U30 and pasted it into the new spreadsheet. I then Saved As (the new spreadsheet) - as a .csv file. Then open this with Notepad, and Edit / Replace to Replace All double-quotes with Nothing and Replace All commas with a space. Now you have a block of data you can copy and paste straight into the polar 1 section of the par file (which for this purpose you have opened with Notepad), but note that when you paste it over the existing data you'll introduce a blank line between this data and the three Separation lines. Delete this blank line.

Let me know if you can't follow any of this. This is similar to the work I used to do, so it's pretty natural for me - but I can see that won't be true for everyone. JSC

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